Atomic cross sections
Cross sections are approximated with semi-analytic expressions, obtained from E.Havlickova but of unknown origin. For the purposes of calculating these cross-sections, any temperatures below 1eV are set to 1eV. The charge exchange cross-section is approximated as:
with units of \([\textrm{m}^3/\textrm{s}]\). Ionisation is calculated as
Recombination rates are calculated using a \(9\times 9\) table of coefficients so is not reproduced here.
Plots of these cross-sections are shown in figure 1. There are a few anomalies with this: charge exchange always has the highest cross-section of any process, and ionisation has a jump at \(20\)eV. The ionisation and charge exchange rates do not depend on density, but recombination does so a typical range of values is shown.